Vol. 19(2018) No. 1



  Nonlinear contractions in metric spaces under locally T-transitive binary relations
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Fixed Point Theory, Volume 19, No. 1, 2018, 13-24, February 1st, 2018

DOI: 10.24193/fpt-ro.2018.1.02

Authors: Aftab Alam and Mohammad Imdad

Abstract: In this paper, we present a variant of Boyd-Wong fixed point theorem in a metric space equipped with a locally T-transitive binary relation, which under universal relation reduces to Boyd-Wong (Proc. Amer. Math. Soc. 20(1969), 458-464) and Jotic (Indian J. Pure Appl. Math. 26(1995), 947-952) fixed point theorems. Also, our results extend several other well-known fixed point theorems such as: Alam and Imdad (J. Fixed Point Theory Appl. 17(2015), no 4, 693-702) and Karapinar and Roldán-López-de-Hierro (J. Inequal. Appl. 2014:522(2014), 12 pages) besides some others.

Key Words and Phrases: -continuity; locally T-transitive binary relations; φ-contractions; -connected sets; fixed point.

2010 Mathematics Subject Classification: 47H10, 54H25.

Published on-line: February 1st, 2018.

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